I. Field of the Invention
This invention relates generally to cardiac monitoring apparatus, and more particularly to a method and apparatus for quantitatively measuring the instantaneous volume of blood contained within a given chamber of the heart whereby stroke volume and cardiac output can be continuously monitored.
II. Discussion of the Prior Art
As is pointed out in my copending application, Ser. No. 362,903, filed Mar. 29, 1982 and entitled: "BIOMEDICAL METHOD AND APPARATUS FOR CONTROLLING THE ADMINISTRATION OF THERAPY TO A PATIENT IN RESPONSE TO CHANGES IN PHYSIOLOGIC DEMAND", the technique of electrical impedance measurement of intravascular volume has been under investigation for over 30 years, but has only recently been applied to the determination of intracardiac volume in humans. In 1953, Rushmer et al in a paper entitled "Intracardiac Plethysmography" (Am. J. Physiol. 174; 171; 1953) discussed an experiment in which electrodes were attached to the walls of both the right and left ventricles of dogs and used to record changes in impedance during contraction. Geddes et al, in a paper entitled "Continuous Measurement of Ventricular Stroke Volume By Electrical Impedance", published in Cardiac Research Center Bulletin, vol. 4, pg. 118 (1966), describes an experiment in which electrodes were sutured to the epicardium of a dog for measuring impedance at 80 kHz during the injection and withdrawal of blood from the animal's with valves sutured closed in vitro. More recently, Baan et al used an 8-ring catheter and a drive frequency of 20 kHz and recorded in dogs a high degree of correlation between left ventricular impedance measurements and stroke volume, the latter being determined simultaneously through the use of an electromagnetic flow meter (Baan et al, "Continuous Stroke Volume and Cardiac Output from Intraventricular Dimensions Obtained With An Impedance Catheter", CardiovasC Res 15; 328; 1981). In a later paper by Baan et al, entitled "Continuous Registration of Relative Left Ventricle Volume in Man" (Circulation 66) (Suppl. II): II-277, 1982, a report is provided on an experiment in which a catheter has been used to continuously record ventricular impedance and relate it to volume in six patients. The first of the aforereferenced Baan et al publications sets out a theoritical basis for the volume determinations based upon impedance measurements.
As a first approximation, the volume of blood that is measured between any two sensing electrodes can be considered to be a cylinder with boundaries defined by the endothelial surfaces of the cardiac walls and by the equally potential surfaces through the electrodes. The total volume of blood within the left ventricular cavity can thus be considered to be a column of the cylinders stacked together. The change in impedance sensed during ventricular contraction in any one of these cylinders is caused by a change in resistance between the two sensing electrodes as a result of a change in the cross-sectional area of the cylinder. The relationship between resistance and cross-sectional area is given by the formula EQU R=.rho.L/A
where R equal resistance, .rho. equals resistivity of blood, L equals the distance between sensing electrodes and A equals the cross-sectional area. For a cylindrical volume where volume (V) is equal to cross-sectional area times length (A.times.L), the above equation may be substituted for resistance EQU R=.rho.L.sup.2 /V
Resistance at end-diastole and end-systole can thus be defined as EQU R.sub.ed =.rho.L.sup.2 /V.sub.ed and R.sub.es =.rho.L.sup.2 /V.sub.es
where "ed" indicates end-diastole and "es" indicates end-systole. By combining these two equations and subtracting the following formula for stroke volume results: ##EQU1##
Thus, for a given cylindrical segment of blood between any two longitudinally spaced sensing electrodes, the change in volume that occurs with ventricular contraction can be determined from the difference in impedance at end-systole and end-diastole. Moreover, since each cylinder of blood within the left ventricle can be thought of as a resistor in series between the driving electrodes, volume measurements for individual cylinders can be added to determine the stroke volume of the whole ventricle.
The theory of impedance volume measurement just presented must be considered an over-simplification since factors critical to accurate measurement have not been addressed. One of the major difficulties encountered with impedance determination of absolute volumes has been in factoring out the contribution of myocardial tissue to measurements of intracardiac electrical impedance. The impedance method of determining ventricular cavity volumes depends on the higher electrical resistivity of myocardial tissue than blood. As a result, the measuring current is primarily contained within the ventricular chamber, and impedance changes should predominantly reflect the time varying quantity of intracavitary blood. Under ideal conditions, if the tissues were a perfect insulator, all of the measuring current would pass only through the ventricular cavity and extremely accurate volume measurements could be made. Support for this concept is derived from impedance measurements of blood volumes contained within a rubber bulb in which correlations of impedance with absolute volumes have been found to be 0.99.
We have determined that the effect of the parallel resistance of the myocardium and surrounding tissue is to decrease the measured resistance and thus add an apparent volume (V.sub.OFFSET) to the actual ventricular volume.
In addition to the above-described contribution of myocardial impedance to impedance volume measurements, there are other problems in the determination of absolute chamber volumes. One such problem concerns the resistivity of blood, which is not constant, and it has been shown to vary with temperature, hematocrit, and blood velocity. Moreover, it is possible that changes in electrolyte concentrations alter resistivity as well.
When a catheter is positioned within a ventricular chamber and a drive potential of a predetermined frequency is applied between a pair of spaced electrodes, where one is proximate the apex of the chamber and the other is proximate the aortic valve, it is found that the electric field lines are not straight, but are outwardly bowed. Similarly, the equipotential lines are not straight but are also bowed so as to intersect the electric field lines at right angles. This pattern also results in a lack of homogeneity in the current density within the ventricular chamber. Because the volume formula =.rho.L.sup.2 /R only applies to regularly shaped cylindrical volumes, when an attempt is made to apply that formula to the actual conditions prevailing when spaced drive electrodes are energized, error is introduced into the ventricular volume measurement. This error is especially acute in the right ventricle due to its shape. The extent of the error can be reduced somewhat by effectively breaking up the volume spanned by the drive electrodes into discrete segments, computing the volume of those individual segments and then summing the individual volume measurements to obtain a total volume as in Baan et al. However, this does not address the inappropriate nature of the cylindrical volume formula for this non-cylindrical situation.